/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 67 What is simple harmonic motion? ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 67

What is simple harmonic motion? Give an example with your description.

Short Answer

Expert verified
Simple Harmonic Motion (SHM) is a type of oscillatory motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. Characteristics of SHM include perpetual motion about a fixed point, highest velocity at equilibrium, and greatest acceleration at maximum displacement. A practical example of SHM is the motion of a simple pendulum.

Step by step solution

01

Definition of Simple Harmonic Motion

Simple Harmonic Motion, abbreviated as SHM, is a type of oscillatory or periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. This can be mathematically represented as \(F = -kx\) where: \(F\) is the restoring force, \(x\) is the displacement from the equilibrium position and \(k\) is a constant.
02

Characteristics of Simple Harmonic Motion

Characteristics of SHM are: 1. The motion is always about a fixed point called the center of motion or equilibrium point, 2. The motion is perpetual unless an external force interferes, 3. The velocity of the object in SHM is highest when it passes the equilibrium point and is zero when it reaches the maximum displacement, 4. The acceleration of the object is highest at the maximum displacement and zero at the equilibrium point.
03

Example of Simple Harmonic Motion

One typical example of simple harmonic motion is a simple pendulum. When a pendulum is displaced from its equilibrium position and released, it swings back and forth due to the restoring force of gravity. The restoring force of the pendulum is proportional to its displacement (represented by the angle) and acts in the opposite direction, making the pendulum's to-and-fro motion a Simple Harmonic Motion.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Explain why, without restrictions, no trigonometric function has an inverse function.

How do we measure the distance between two points, \(A\) and \(B,\) on Earth? We measure along a circle with a center, \(C,\) at the center of Earth. The radius of the circle is equal to the distance from \(\mathrm{C}\) to the surface. Use the fact that Earth is a sphere of radius equal to approximately 4000 miles to solve Exercises 93-96. If \(\theta=10^{\circ},\) find the distance between \(A\) and \(B\) to the nearest mile.

Use a graphing utility to graph two periodsof the function. Use a graphing utility to graph \(y=\sin x\) and \(y=x-\frac{x^{3}}{6}+\frac{x^{5}}{120}\) in a \(\left[-\pi, \pi, \frac{\pi}{2}\right]\) by \([-2,2,1]\) viewing rectangle. How do the graphs compare?

Find the slant asymptote of $$f(x)=\frac{2 x^{2}-7 x-1}{x-2}$$

Let \(f(x)=\left\\{\begin{array}{ll}{x^{2}+2 x-1} & {\text { if } x \geq 2} \\\ {3 x+1} & {\text { if } x<2}\end{array}\right.\) Find \(f(5)-f(-5)\)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.